Two different approaches to intergranular crack propagation in brittle polycrystals are contrasted. Crack paths resulting from a method that allows a detailed description of the stress field within a polycrystal are compared to cracks dictated by topological considerations. In the first approach, a fracture path is determined with a Generalized Finite Element Method for polycrystals considering isotropic elastic grains. In the second approach a fracture path is generated using Dijkstra's shortest path algorithm. This algorithm yields minimum fracture energy crack paths. A series of simulations is performed to assess the influence of the method of analysis on the crack path.